Tiny Periodicness

True or False?

Every function ( $f: \mathbb{R} \rightarrow \mathbb{R}$ ) which has a period has a smallest period.

A period of $f: \mathbb{R} \rightarrow \mathbb{R}$ is a number $T > 0$ such that $f(x)=f(x+T) \space \forall x \in \mathbb{R}$ .